Hydrodynamic theory of biaxial nematics
TL;DR: In this article, a nonlinear hydrodynamic theory is presented which emphasizes the fundamental similarities between the different biaxial nematics and clarifies the changes in the static and dynamic behavior as the discrete symmetries vary.
Abstract: Biaxial nematics are usually regarded as characterized by a symmetric, traceless tensor having three different eigenvalues. It is argued that this definition is too restrictive and that a natural extension would embrace any system that breaks all three rotational symmetries while preserving translational invariance. That is, biaxial nematics need not have orthorhombic symmetry, but may be triclinic, hexagonal, cubic, or even isotropic. A non-linear hydrodynamic theory is presented which emphasizes the fundamental similarities between the different biaxial nematics and clarifies the changes in the static and dynamic behavior as the discrete symmetries vary. The Goldstone modes of any biaxial nematics are identified as two pairs of orbital waves with a complex, and one orbital diffusion with a purely imaginary, dispersion relation. If the longitudinal and transverse variables decouple, it is the longitudinal rotation angle that diffuses.
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TL;DR: A complete continuum mechanical theory for granular media, including explicit expressions for the energy current and the entropy production, is derived and explained in this paper, where the authors refer to the theory as GSH.
Abstract: A complete continuum mechanical theory for granular media, including explicit expressions for the energy current and the entropy production, is derived and explained. Its underlying notion is: granular media are elastic when at rest, but turn transiently elastic when the grains are agitated—such as by tapping or shearing. The theory includes the true temperature as a variable, and employs in addition a granular temperature to quantify the extent of agitation. A free energy expression is provided that contains the full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. We refer to the theory as GSH, for granular solid hydrodynamics. In the static limit, it reduces to granular elasticity, shown previously to yield realistic static stress distributions. For steady-state deformations, it is equivalent to hypoplasticity, a state-of-the-art engineering model.
117 citations
TL;DR: Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain this paper.
Abstract: Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived based on the hypothesis that granular medium turns transiently elastic when deformed. This theory includes both the true and the granular temperatures, and employs a free energy expression that encapsulates a full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. For the special case of stationary granular temperatures, the derived hydrodynamic theory reduces to {\em hypoplasticity}, a state-of-the-art engineering model.
115 citations
Cites methods from "Hydrodynamic theory of biaxial nema..."
...The hydrodynamic approach [26, 27] has since been successfully employed to account for many condensed systems, including liquid crystals [28, 29, 30, 31, 32, 33, 34], superfluid (3)He [35, 36, 37, 38, 39, 40], superconductors [41, 42, 43], macroscopic electro-magnetism [44, 45, 46, 47] and ferrofluids [48, 49, 50, 51, 52, 53, 54, 55, 56]....
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TL;DR: In this paper, optical studies have been carried out on a nematogenic copper complex, which incorporates the features of both rod-like and disk-like molecules, and conoscopic figures have been presented demonstrating the occurrence of a biaxial nematic phase in the pure complex, the uniaXial-biaxial (Na-Nb) transition in binary mixtures, and the temperature variation of the biaaxiality near this transition.
Abstract: Optical studies have been carried out on a nematogenic copper complex, which incorporates the features of both rod-like and disk-like molecules. Conoscopic figures are presented demonstrating (i) the occurrence of a biaxial nematic phase in the pure complex, (ii) the uniaxial-biaxial (Na-Nb) transition in binary mixtures, and (iii) the temperature variation of the biaxiality near this transition. The I-Na-Nb phase diagram has been studied for the binary system.
105 citations
01 Jan 1996
TL;DR: In this article, the hydrodynamic and electrohydrodynamic equations for uniaxial nematic liquid crystals were derived for sufficiently small frequencies in the limit of long wavelengths.
Abstract: We present the hydrodynamic and electrohydrodynamic equations for uniaxial nematic liquid crystals and explain their derivation in detail. To derive hydrodynamic equations, which are valid for sufficiently small frequencies in the limit of long wavelengths, one identifies first the hydrodynamic variables, which come in two groups: quantities obeying conservation laws and variables associated with spontaneously broken continuous symmetries. As variables that characterize the spontaneously broken continuous rotational symmetries of a nematic liquid crystal we have the deviations from the preferred direction, which is characterized by the director, a unit vector that does not distinguish between head and tail.
89 citations
TL;DR: In this paper, a continuum theory is used to study ordering in liquid crystal nanodroplets and the free energy functional that describes the system is minimized using an Euler-Lagrange approach and an unsymmetric radial basis function method.
Abstract: A continuum theory is used to study ordering in liquid crystal nanodroplets. The free energy functional that describes the system is minimized using an Euler–Lagrange approach and an unsymmetric radial basis function method. The equilibrium morphology in nanodroplets is shown to represent a delicate balance between bulk and surface contributions; when the radius of the droplet reaches a critical value, that balance is altered and the droplet undergoes a transition. By controlling the anchoring conditions at the droplet's surface, one can control the radius where the transition occurs and even prepare metastable droplets where small perturbations can trigger a morphological transition. The results of the theory are shown to be consistent with recent experimental observations on monodisperse nematic liquid crystal nanodroplets.
57 citations